## declining waterlevels in a drainage ditch

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Schot
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### declining waterlevels in a drainage ditch

How can I model the (surface) water level in a drainage ditch which is filled by outflowing groundwater?
I model a section of a parcel with two drainage ditches. Lower section boundary has a constant upward seepage flux and the ditches have a constant pressure Boundary Condition (fluctuating between summer and winter resp. +0,5 and + 0,3).
Now I want to change the BC of the ditches in summer: this is no constant pressure anymore, but the level in the ditch is a result of the seepage of groundwater in the ditch (which is a function of the upward seepage flux from the lower boundary and the net-precipitation at the upper boundary). The level in the ditch thus may fluctuate depending on the outflow into the ditch.
--> My question is: How do I model this, cq. what kind of boundary condition should I take in the ditches?

[ In the book "Modelling variably saturated flow with HYDRUS-2D" by Rassam, Simunek and van Genuchten (second edition 2004) I found an Example Application for Fluctuating Stream Level (page 4.1), which I think is maybe usable for my problem. In the example they first model the Rising stream level (in my case that is the higher winter-water level in the ditch of +0,5m), and then make a new model for the Falling stage of the river level (in my case of the ditch level) with a Seepage Face. However, this gives strange results, as a Seepage Face in the ditches immediately (after 1 time-step) results in a dry ditch (which is maybe not surprising because seepage face uses Presuure heads=o at the bundary of the ditch).
Another option is maybe something with "ponding" in the ditch up to a certain prescribed level, but how do I do this? ]

Thanks for your help!

Regards,
Paul

Jirka
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Location: Riverside, CA
I'm traveling in Israel. I will answer when I come back to Riverside next week. Jirka

Jirka
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Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA
a) Note that the book by Rassam et al. (2004) describes the older version of HYDRUS, i.e., HYDRUS-2D, and that this older version did not have many system-dependent boundary conditions, which are now available in the new version.

b) On the Edit bar there is a command “BDRC Options”. Here you can select multiple system-dependent boundary conditions that may apply to your situation. In you case I would use the option “Switch the boundary condition from time-variable pressure head to seepage face when the specified nodal pressure is negative”. When you specify a positive pressure head, the model will assume that there is water in the furrow up to this height and seepage face above this height. Once you specify a negative pressure head, the code will assume seepage face in the entire furrow (for your upward seepage flow).

Jirka

Schot
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Just back from holiday and saw your reply. Thanks Jirka!

However, I have still some questions with respect to your remark "once you specify a negative pressure head, the code will assume seepage face in the entire furrow"?

a) Does this mean I myself have to specify a negative head of e.g. -1 for the time period of the summer months (in which no constant pressure exists anymore in the ditch, but a 'free'surface water table')? And does the value of the negative head matter?

b) If the code assumes seepage face in the entire furow (after specifying a negative head) doesn't this mean it then takes a pressure of 0 (=atmospheric pressure) in the ditch? I already tried this in the "old"2D -version and it resulted in an instant complete draining of all water from the soil up to the level of the bottom of the furrow. This does not seem realistic to me.

In anticipation of your answer, I already have some thoughts about alternative solutions below. Maybe yu can comment on these too.

Alternative 1)
Model the summer period with the ditch filled in with soil with very high permeability (as to approach "surface water with low resistance). Initial conditions are taken from the last winter time step. This will make the ditch show water levels comparable to that in the soil adjacent, and which depends on the balance between the negative net precipitation flux (ET is higher than P in summer) from above, and the positive seepage flow from below.

Alternative 2)
Use the CW2d model to assume ponding in the furrow/ditch. At the start of summer the "ponding" in the ditch is set to +0,3 (which is the winter surface water level in the ditch). Then see if the ponding depth goes down, or up (and maybe eventually overflows the whole surface when exceeding the edges of the ditch).

By the way: to better understand the geometry one may check a similar exercise in J.Hydrology 2004 Schot et. al. The dynamic form of rainwater lenses in drained fens.
(Also found at http://www.uu.nl/uupublish/content/J.Hydrl_2004.pdf)

Jirka
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Joined: Sat Mar 16, 2002 3:47 pm
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Location: Riverside, CA
a) Correct. For period when there is not water in the furrow, you need to specify a negative head (any value).

b) No. This is a new special option (i.e., the seepage face on the time-variable head boundary when the pressure head is negative) in HYDRUS (2/3D), which was not available in HYDRUS-2D and thus codes should behave differently. The code will set pressure head equal to zero only on the part of the domain where water has tendency to leave the profile (i.e., where the pressures are positive in the transport domain around this point), i.e., on active seepage face. Pressure heads should remain negative elsewhere, i.e., only potential seepage face.

c) Ad Alternative 1: This was possible way of dealing with this problem in the older HYDRUS-2D, where the special boundary options were not available.

d) Ad Alternative 2: I do not recall how ponding option in CW2D was implemented. This special option was included by Guenter Langergraber. I believe that it dealt with individual boundary nodes independently.

Thanks for the reference. I do have the paper.

Jirka

Schot
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Dear Jirka,

I tried your suggestion with the negative pressure in the ditches/furrow in summer, but the model crashed because "ORTHOMIN termintes- too many iterations (about 5000)".

I also tried my alternative with the ditches filled in with soil using initial conditions imported from the preceding end-of-winter simulation. Again the model crashed: "ORTHOMIN-too many iterations". I changed Initial timestep and Minimum timestep from 0,1 to 0,001 but this doesn't solve the problem.

Do you have any suggestions how to avoid the crashes?

Thanks,

Paul

Jirka
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Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA
ORTHOMIN error - this means that the matrix solver can not solve the system of equation, that it is a singular matrix. This usually means that the problem is not well defined. I would try too things (allow smaller minimum time step (donw to 1 s), increase pressure head tolerance (1, but up to 5 cm).

Jirka